This is an experimental study of algorithms for the shortest-path feasibility
problem: Given a directed weighted graph, find a negative cycle or present a
short proof that none exists. We study previously known and new algorithms. Our
testbed is more extensive than those previously used, including both static and
incremental problems, as well as worst-case instances. We show that, while no
single algorithm dominates, a small subset (including new algorithms) has very
robust performance in practice. Our work advances the state of the art in the
area.